The growth and properties of galaxies are thought to be closely connected to the ones of their host dark matter haloes. Despite the importance of this so-called galaxy-halo connection, the potential role of dark matter haloes in regulating observed galaxy properties remains yet to be fully understood. In this work, we derive the ages, metallicites, and [Mg/Fe] abundances from optical spectra from the Sloan Digital Sky Survey of nearby central galaxies, and study them in terms of their host haloes. We investigate how the scatter in the stellar-to-halo mass relation and the velocity dispersion-halo mass relation correlates with these stellar population parameters. In addition, we also study the differences when distinguishing between different galaxy morphologies and environments. We find that the ages and chemical enrichment of galaxies are not fully determined by their stellar masses or velocity dispersion, but also depend on the mass of the host haloes. Our findings suggest that the velocity dispersion is the best proxy of the stellar population parameters with halo mass playing a secondary yet noticeable role. We interpret that the origin of the correlation between the scatter of these relations and the ages and metallicities might be related to different halo formation times.